1,721,110 research outputs found
How Tick Size Affects the High Frequency Scaling of Stock Return Distributions
No full textWe study the high frequency scaling of the distributions of returns for stocks traded at NASDAQ market as a function of the tick–to–price ratio. The tick–to–price ratio is a measure of an effective tick size. We find dramatic differences between distributions for assets with large and small tick–to–price ratio. The presence of returns clustering is evident for large tick size assets. The statistical differences between large and small tick size assets appear to reduce at higher time scales of observation. A possible way to explain returns dynamics for large tick size assets is the coupling of returns with bid–ask spread dynamics. A simple Markov–switching model is able to reproduce the properties of the distribution of returns for large tick size assets
Order flow and price formation
Full text linkI present an overview of some recent advancements on the empirical analysis and theoretical modeling of the process of price formation in financial markets as the result of the arrival of orders in a limit order book exchange. After discussing critically the possible modeling approaches and the observed stylized facts of order flow, I consider in detail market impact and transaction cost of trades executed incrementally over an extended period of time, by comparing model predictions and recent extensive empirical results. I also discuss how the simultaneous presence of many algorithmic trading executions affects the quality and cost of trading
The risk approach to portfolio construction
No full textLo studio della mia tesi riguarda i modelli di selezione del portafoglio finanziario secondo il criterio del Risk Parity. Questi modelli hanno avuto un certo successo dopo la recente crisi finanziaria per il modo in cui distribuiscono il rischio tra gli asset che compongono il portafoglio finanziario. I primi autori che hanno formalizzato l'argomento sono Sébastien Maillard, Thierry Roncalli e Jérome Teiletche (2008). L'approccio del Risk Parity richiede la contribuzione al rischio di ciascun titolo nella stessa quantità, tendendo cosi a massimizzare la diversificazione del rischio. Nella tesi ho elencato le proprietà teoriche del modello, confrontando queste proprieta con quelle degli altri modelli.Nella maggior parte dei modelli di Risk Parity presenti in letteratura si utilizza come misura del rischio la deviazione standard dei rendimenti. E' tuttavia possibile applicare il modello di Risk Parity con una misura di rischio diversa: il Conditional Value-at Risk (CVaR). Questa è una misura coerente e convessa, alla quale si può quindi applicare la scomposizone di Eulero per le funzioni omogenee di primo grado. La scomposizione richiede il calcolo delle derivate parziali della misura di rischio scelta. Questo modello è stato utilizzato da Kris Boudt, sotto l'ipotesi che i rendimenti si distribuiscano come una normale multivariata nelle stime delle quote degli assets, ipotesi che costituisce un'approssimazione poco realistica della realtà. Il modello di Risk Parity con la misura di rischio CVaR si può applicare anche per rendimenti distribuiti in modo diverso da una normale multivariata. Questo è possibile grazie ad approssimazioni nel calcolo delle derivate parziali del CVaR. Nella tesi confronto i portafogli individuati con il Risk Parity con le misure diverse di rischio (deviazione standard e Conditional Value at Risk). Ho sviluppato un metodo per il calcolo del portafoglio di Risk Parity con il CVaR confrontandolo con quello proposto in un lavoro recente di Colucci (2013).
I modelli sviluppati sono stati applicati ai dati con frequenza settimanale con opportuna ampiezza dei periodi considerati in modo tale da avere una buona approssimazione del Risk Parity con il CVaR.
Nella tesi ho sviluppato alcuni modelli di ottimizzazione per la selezione di portafoglio secondo il modello di Risk Parity. I modelli sono stati implementati con il software scientifico Matlab che è molto efficace nel calcolo di grandi quantità di dati. Nell'impossibilità di applicare direttamente i vincoli di cardinalità ai modelli di Risk Parity, ossia di limitare la scelta dei titoli ad un numero inferiore ad un K prefissato, ho ipotizzato di effettuare una preselezione dei titoli selezionando quei titoli presenti nei portafogli di minimo rischio rispetto alla misura di rischio considerata. In questo modo si possono creare portafogli con meno titoli ma ben diversificati.
I principali dataset utilizzati sono i seguenti:
a) Commodities (8 assets) Sample Period: 01/01/2000-24/09/2014
(Gold,Silver,Oil,Heat Oil,Euro,Pounds,Australian Dollar,New Zealand Dollar)
b) Stocks Sample Period: 01/01/2000-01/07/2014
1.DAX30 (26 stocks)
2.CAC40 (32 stocks)
3.Eurostoxx50 (44 stocks)
4.FTSE100 (77 stocks)
5.Nikkei225 (188 stocks)
c) Euro Gov. Bond (Govt 7-10 Yr) (9 assets) Sample Period: 01/01/2000-18/12/2013
d) Mixed portfolios 37 assets Sample Period: 01/01/2000-18/12/2013
(Dax30 + Euro Government Bond+ Gold+Silver)
I risultati conclusivi delle analisi condotte mostrano empiricamente che il Risk Parity con il CVaR ha una rischiosità maggiore del CVaR, ma inferiore al Risk Parity-Naive ed il modello uniforme. Inoltre, la creazione di portafogli misti può garantire non solo una buona diversificazione ma anche una discreta performance. Confrontando la performance del Risk Parity con la deviazione standard e quella con il CVaR possiamo dire che non c’è una differenza significativa, ma ricordiamo che il CVaR ha migliori proprietà in quanto è una misura coerente e convessa
Price Dynamics in a Markovian Limit Order Market
Full text linkWe propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantities of interest such as the distribution of the duration between price changes, the distribution and autocorrelation of price changes, and the probability of an upward move in the price, conditional on the state of the order book. We study the diffusion limit of the price process and express the volatility of price changes in terms of parameters describing the arrival rates of buy and sell orders and cancelations. These analytical results provide some insight into the relation between order flow and price dynamics in order-driven markets.limit order book, market microstructure, queueing, diffusion limit, high-frequency data, liquidity, duration analysis, point process
Mathematical and Computational Aspects of Machine Learning
No full textThe past few years have witnessed an impressive growth and development of machine learning methods. Enhanced by large collected databases and improved computational power, these techniques have made spectacular progress in fields like image recognition and have even reached the ability to surpass humans in certain tasks and in games like Go.
Still, the conceptual mechanisms on which such forms of learning work are largely not understood. Moreover, there is a complete lack of prediction ability, not only in the efficiency of machine learning, but also on its ability to work at all on a new problem. All this calls for a strong commitment on the part of the mathematical community. The present school aims at connecting international experts at the forefront of research on the mathematical and computational aspects of the problem with the interested scholars, especially the young generations.
Courses
The programme includes 5 minicourses of 6 hours each.
Lectures will be delivered by experts of international standing.
Deadline for registration: 31st August 2019.
Admission to the courses will be notified by 15th September after the Scientific Committee's decision.
Jean Barbier
Philipp Grohs
Gabriel Peyré
Lars Ruthotto
Stefano Soatt
Toward new metrics assessing air traffic interaction
No full textIn ATM systems, the massive number of interacting entities makes it difficult to predict the system-wide effects that innovations might have. Here, we present the approach proposed by the project Domino to assess such effects and identify the impact that innovations might bring for the different stakeholders, based on agent-based modelling and complex network science. Domino will model scenarios mirroring different system innovations which change the agents’ actions and behaviour. Suitable network metrics are needed to evaluate the effect of innovations on the network functioning. We review existing centrality and causality metrics and show their limitations in characterising the network by applying them to a dataset of US flights. We finally suggest improvements that should be introduced to obtain new metrics answering to Domino’s needs
How Tick Size Affects the High Frequency Scaling of Stock Return Distributions
No full textWe study the high frequency scaling of the distributions of returns for stocks traded at NASDAQ market as a function of the tick-to-price ratio. The tick-to-price ratio is a measure of an effective tick size. We find dramatic differences between distributions for assets with large and small tick-to-price ratio. The presence of returns clustering is evident for large tick size assets. The statistical differences between large and small tick size assets appear to reduce at higher time scales of observation. A possible way to explain returns dynamics for large tick size assets is the coupling of returns with bid-ask spread dynamics. A simple Markov- switching model is able to reproduce the properties of the distribution of returns for large tick size assets
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Linear models for the impact of order flow on prices. I. History dependent impact models
No full textMarket impact is a key concept in the study of financial markets and several models have been proposed
in the literature so far. The propagator model posits that the price at high frequency time scales is a linear
combination of the signs of the past executed market orders, weighted by a so-called propagator function.
This model needs to be extended since prices are a priori influenced not only by the past order flow,
but also by the past realisation of returns themselves. In this paper, we propose a two-event framework,
where price-changing and non price-changing events are considered separately. We show that two-event
propagator models provide a remarkable improvement of the description of the market impact, especially
for large tick stocks, where the events of price changes are very rare and very informative. Specifically
the extended approach captures the excess anti-correlation between past returns and subsequent order
flow which is missing in one-event models
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